Solving Maxwell's equations using fractional wave equations

2006 ◽  
Author(s):  
K.F. Warnick ◽  
P. Russer
Keyword(s):  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Fractional Wave Equations

WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS

2012 ◽  
Vol 14 (05) ◽  
pp. 1250032 ◽  
Author(s):  
BRUNO FRANCHI ◽  
MARIA CARLA TESI
Keyword(s):  
Vector Potential ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Evolution Equations ◽  
Differential Forms ◽  
Higher Order ◽  
Carnot Groups ◽  
New Class ◽  
Euclidean Setting

In this paper we define Maxwell's equations in the setting of the intrinsic complex of differential forms in Carnot groups introduced by M. Rumin. It turns out that these equations are higher-order equations in the horizontal derivatives. In addition, when looking for a vector potential, we have to deal with a new class of higher-order evolution equations that replace usual wave equations of the Euclidean setting and that are no more hyperbolic. We prove equivalence of these equations with the "geometric equations" defined in the intrinsic complex, as well as existence and properties of solutions.

scholarly journals Extension of the electrodynamics in the presence of the axion and dark photon

2019 ◽  
Vol 34 (03n04) ◽  
pp. 1950012 ◽  
Author(s):  
Fa Peng Huang ◽  
Hye-Sung Lee
Keyword(s):  
Magnetic Field ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Dark Photon

We present the extended electrodynamics in the presence of the axion and dark photon. We derive the extended versions of Maxwell’s equations and dark Maxwell’s equations (for both massive and massless dark photons) as well as the wave equations. We discuss the implications of this extended electrodynamics including the enhanced effects in the particle conversions under the external magnetic or dark magnetic field. We also discuss the recently reported anomaly in the redshifted 21 cm spectrum using the extended electrodynamics.

scholarly journals Internal stabilization of Maxwell's equations in heterogeneous media

2005 ◽  
Vol 2005 (7) ◽  
pp. 791-811 ◽  
Author(s):  
Serge Nicaise ◽  
Cristina Pignotti
Keyword(s):  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Heterogeneous Media ◽  
Space Variable ◽  
Smooth Boundary ◽  
Variable Coefficients ◽  
Bounded Region ◽  
Scalar Wave ◽  
Internal Stabilization

We consider the internal stabilization of Maxwell's equations with Ohm's law with space variable coefficients in a bounded region with a smooth boundary. Our result is mainly based on an observability estimate, obtained in some particular cases by the multiplier method, a duality argument and a weakening of norm argument, and arguments used in internal stabilization of scalar wave equations.

Note on the Antecedents of Clerk-Maxwell's Electrodynamical-Wave-Equations

1895 ◽  
Vol 20 ◽  
pp. 213-214 ◽  
Author(s):  
Tait
Keyword(s):  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Magnetic Force ◽  
Elastic Solid ◽  
Point Of View ◽  
Polarised Light ◽  
The Way

The first obvious difficulty which presents itself, in trying to derive Clerk-Maxwell's equations from those of the elastic-solid theory, appears in the fact that the latter, being linear, do not impose any relations among simultaneous disturbances. Thus, for instance, they indicate no reason for the associated disturbances which, in Maxwell's theory, constitute a ray of polarised light. Hence it appears that we must look on the vectors of electric and magnetic force, if they are to be accounted for on ordinary dynamical principles, as being necessary concomitants, qualities, or characteristics of one and the same vector-disturbance of the ether, and not themselves primarily disturbances. From this point of view the disturbance, in itself, does not correspond to light, and may perhaps not affect any of our senses. And the very form of the elastic equation at once suggests any number of sets of two concomitants of the desired nature, which are found to be related to one another in the way required by Maxwell's equations.

scholarly journals DIFFRACTION OF BLOCH WAVE PACKETS FOR MAXWELL'S EQUATIONS

2013 ◽  
Vol 15 (06) ◽  
pp. 1350040 ◽  
Author(s):  
GRÉGOIRE ALLAIRE ◽  
MARIAPIA PALOMBARO ◽  
JEFFREY RAUCH
Keyword(s):  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Plane Waves ◽  
Approximate Solutions ◽  
Bloch Wave ◽  
System Structure ◽  
Periodic Medium ◽  
Scalar Wave ◽  
Infinite Dimensional

We study, for times of order 1/h, solutions of Maxwell's equations in an [Formula: see text] modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct accurate approximate solutions of three scale WKB type. The leading profile is both transported at the group velocity and dispersed by a Schrödinger equation given by the quadratic approximation of the Bloch dispersion relation. A weak ray average hypothesis guarantees stability. Compared to earlier work on scalar wave equations, the generator is no longer elliptic. Coercivity holds only on the complement of an infinite-dimensional kernel. The system structure requires many innovations.

Relativistic Wave Equations

2019 ◽  
pp. 25-42
Author(s):  
Michael E. Peskin
Keyword(s):  
Dirac Equation ◽  
Maxwell’S Equations ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Gordon Equation ◽  
Relativistic Wave Equations ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Klein Gordon ◽  
Klein Gordon Equation

This chapter presents the wave equations that govern the behavior of quantum mechanical particles with spin 0, 1/2, and 1 in relativistic theories. These equations are the Klein-Gordon equation, the Dirac equation, and Maxwell’s equations.

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